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Announcements. Project 3 code & artifact due Tuesday Final project proposals due noon Wed (by email) One-page writeup (from project web page), specifying: Your team members Project goals. Be specific. Describe the input and output.
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Announcements • Project 3 code & artifact due Tuesday • Final project proposals due noon Wed (by email) • One-page writeup (from project web page), specifying: • Your team members • Project goals. Be specific. Describe the input and output. • Brief description of your approach. If you are implementing or extending a previous method, give the reference and web link to the paper. • Will you be using helper code (e.g., available online) or will you implement it all yourself? • Evaluation method. How will you test it? Which test cases will you use? • Breakdown--what will each team-member do? Ideally, everyone should do something imaging/vision related (it's not good for one team member to focus purely on user-interface, for instance). • Special equipment that will be needed. We may be able to help with cameras, tripods, etc. TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAA
Stereo • Readings • Szeliski, Chapter 10 (through 10.5) Single image stereogram, by Niklas Een
Public Library, Stereoscopic Looking Room, Chicago, by Phillips, 1923
Woman getting eye exam during immigration procedure at Ellis Island, c. 1905 - 1920, UCR Museum of Phography
Mark Twain at Pool Table", no date, UCR Museum of Photography
Anaglyphs online • I used to maintain of list of sites, but too hard to keep up to date. Instead, see wikipedia page: • http://en.wikipedia.org/wiki/Anaglyph_image • A free pair of red-blue stereo glasses can be ordered from Rainbow Symphony Inc • http://www.rainbowsymphony.com/freestuff.html
Stereo scene point image plane optical center
Stereo • Basic Principle: Triangulation • Gives reconstruction as intersection of two rays • Requires • camera pose (calibration) • point correspondence
epipolar line epipolar line epipolar plane Stereo correspondence • Determine Pixel Correspondence • Pairs of points that correspond to same scene point • Epipolar Constraint • Reduces correspondence problem to 1D search along conjugateepipolar lines • Java demo: http://www.ai.sri.com/~luong/research/Meta3DViewer/EpipolarGeo.html
l l’ p p’ Fundamental matrix • Let p be a point in left image, p’ in right image • Epipolar relation • p maps to epipolar line l’ • p’ maps to epipolar line l • Epipolar mapping described by a 3x3 matrix F • It follows that
Fundamental matrix • This matrix F is called • the “Essential Matrix” • when image intrinsic parameters are known • the “Fundamental Matrix” • more generally (uncalibrated case) • Can solve for F from point correspondences • Each (p, p’) pair gives one linear equation in entries of F • 8 points give enough to solve for F (8-point algorithm) • see Marc Pollefey’s notes for a nice tutorial
Stereo image rectification • reproject image planes onto a common • plane parallel to the line between optical centers • pixel motion is horizontal after this transformation • two homographies (3x3 transform), one for each input image reprojection • C. Loop and Z. Zhang. Computing Rectifying Homographies for Stereo Vision. IEEE Conf. Computer Vision and Pattern Recognition, 1999.
Stereo matching algorithms • Match Pixels in Conjugate Epipolar Lines • Assume brightness constancy • This is a tough problem • Numerous approaches • A good survey and evaluation: http://www.middlebury.edu/stereo/
For each epipolar line For each pixel in the left image • Improvement: match windows • This should look familar... Your basic stereo algorithm • compare with every pixel on same epipolar line in right image • pick pixel with minimum match cost
W = 3 W = 20 Window size • Smaller window • Larger window • Effect of window size • Better results with adaptive window • T. Kanade and M. Okutomi,A Stereo Matching Algorithm with an Adaptive Window: Theory and Experiment,, Proc. International Conference on Robotics and Automation, 1991. • D. Scharstein and R. Szeliski. Stereo matching with nonlinear diffusion. International Journal of Computer Vision, 28(2):155-174, July 1998
Stereo results • Data from University of Tsukuba • Similar results on other images without ground truth Scene Ground truth
Results with window search Window-based matching (best window size) Ground truth
Better methods exist... • State of the art method • Boykov et al., Fast Approximate Energy Minimization via Graph Cuts, • International Conference on Computer Vision, September 1999. Ground truth • For the latest and greatest: http://www.middlebury.edu/stereo/
Stereo as energy minimization • What defines a good stereo correspondence? • Match quality • Want each pixel to find a good match in the other image • Smoothness • If two pixels are adjacent, they should (usually) move about the same amount
Stereo as energy minimization • Expressing this mathematically • Match quality • Want each pixel to find a good match in the other image • Smoothness • If two pixels are adjacent, they should (usually) move about the same amount • We want to minimize • This is a special type of energy function known as an MRF (Markov Random Field) • Effective and fast algorithms have been recently developed: • Graph cuts, belief propagation…. • for more details (and code): http://vision.middlebury.edu/MRF/ • Great tutorials available online (including video of talks)
X z x x’ f f baseline C C’ Depth from disparity
Video View Interpolation • http://research.microsoft.com/users/larryz/videoviewinterpolation.htm
Real-time stereo • Used for robot navigation (and other tasks) • Several software-based real-time stereo techniques have been developed (most based on simple discrete search) • Nomad robot searches for meteorites in Antartica • http://www.frc.ri.cmu.edu/projects/meteorobot/index.html
Stereo reconstruction pipeline • Steps • Calibrate cameras • Rectify images • Compute disparity • Estimate depth • Camera calibration errors • Poor image resolution • Occlusions • Violations of brightness constancy (specular reflections) • Large motions • Low-contrast image regions What will cause errors?
camera 1 camera 1 projector projector camera 2 Active stereo with structured light • Project “structured” light patterns onto the object • simplifies the correspondence problem Li Zhang’s one-shot stereo
Laser scanning • Optical triangulation • Project a single stripe of laser light • Scan it across the surface of the object • This is a very precise version of structured light scanning • Digital Michelangelo Project • http://graphics.stanford.edu/projects/mich/
Laser scanned models • The Digital Michelangelo Project, Levoy et al.
Laser scanned models • The Digital Michelangelo Project, Levoy et al.
Laser scanned models • The Digital Michelangelo Project, Levoy et al.
Laser scanned models • The Digital Michelangelo Project, Levoy et al.
Laser scanned models • The Digital Michelangelo Project, Levoy et al.
Spacetime Stereo Li Zhang, Noah Snavely, Brian Curless, Steve Seitz http://grail.cs.washington.edu/projects/stfaces/